Claude Finds 663 Theorem Candidates in Gödel's Notebooks, 400 Machine-Verified
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TL;DR
Claude pulled 663 theorem candidates out of Kurt Gödel's 1,009-page workbooks, and the Coq proof assistant verified about 400 of them exactly as stated, The Guardian reported on Nov 13. The workbooks, 16 volumes of logic Gödel kept in the early 1940s, are written largely in Gabelsberger, a German shorthand that was already obsolete when Gödel used it. A University of Helsinki team led by Jan von Plato had been reading them since 2017, at about a page a week. Given his transcriptions, his six earlier books on Gödel and the secondary literature, Claude returned a 650-page digest of the whole corpus in a couple of days.
Nine years at a page a week
Gödel published his incompleteness theorems in 1931 and comparatively little afterwards. The unpublished leftovers run to tens of thousands of pages. The 16 workbooks from the early 1940s are 1,009 of the densest: logic and mathematics, much of it in Gabelsberger, a stenography system nobody has taught at scale in a century.
Von Plato opened the project in 2017, facing mandatory retirement at Helsinki, with a €2.5m European Research Council grant. He taught himself the shorthand and counts six people alive who can read it. His team's rate: about a page a week, roughly 50 pages a year, which makes the workbooks alone a 20-year read at their pace.
What Claude actually did
The model never saw the shorthand. At an August conference in France on AI and theorem proving, computer scientists suggested von Plato bring in Claude. Back in Helsinki, he supplied the model with his own transcriptions, the six books he had already written on Gödel (his Gödel scholarship includes the 2020 volume Can Mathematics Be Proved Consistent?), and the secondary literature. A couple of days later he had a 650-page explanation of the whole corpus, which his team then controlled page for page.
Von Plato's comparison gets at why the speedup happened at all: "Humans read one page at a time and we tend to forget things. It takes us a year to read about 50 pages. We just are not able to keep in mind all the different parts. The AI can connect all the pieces in a thousand pages. It can see all of Gödel's writings as one piece." His team reads the archive like someone doing a jigsaw from memory, one piece delivered a week. Claude tipped the whole box onto the table.
The 663, the 400 and the 50
Von Plato asked Claude to extract every theorem in the workbooks that Gödel had proved, sketched a proof for, or held an idea toward: 663 entries came back. Coq then did the sorting. About 400 verified as stated. About 200 needed repair, a statement made more precise or an assumption added. About 50 were false, and Gödel pre-reviewed some of that class himself: the margins carry his own "falsch!" and "schlecht!", so the false entries are in historic company.
The haul is bigger than a count. On Claude's reading, which von Plato endorses, the workbooks contain dozens of anticipations of results not known until the 1970s and 80s, plus 14 themes in logic that nobody has pursued in the 80-plus years since they were written down.
The proof Gödel could not reconstruct
In 1966 Paul Cohen won the Fields Medal for proving the independence of the continuum hypothesis and the axiom of choice. Gödel responded that he had the axiom-of-choice result in the 1940s, and when colleagues pressed him for the proof, he could not rebuild it from his notes.
Von Plato set Claude exactly this question first. The reconstructed proof came back one step short of done: one definition Gödel used was wrong, and the correct one sits two years earlier in the same workbooks. With that fix, the proof passed Coq. "He was just one step away," von Plato said, adding that the architecture is wonderful, with results across set theory following one uniform pattern. He believes publication in the 1940s would have won Gödel the Fields Medal.
Historians get the last word
Joel David Hamkins, professor of logic at Notre Dame, has not seen Claude's reconstruction. If it stands, he told the paper, "it is remarkable and historically interesting. Although how much is Claude and how much is Gödel is a job for the historians." His warning on credit: "The fact that there are things in there that resemble [Cohen's proof] does not mean he had it. It shows he was on the path. You don't get credit for work you don't tell anyone about."
Three caveats belong next to every number above. The 663 are candidates, ranging from finished proofs to bare ideas. Every figure comes from von Plato's account in an interview, backed by the Coq runs, with no published paper yet. And the model's contribution is entangled with the human's; Hamkins's question is open by design. The next corpus is already queued: Gödel's physics and cosmology notebooks, which von Plato calls unknown territory.
If you own a corpus like this
The transferable part is the division of labor. One of the six people alive who can read the script does the reading. The model does the remembering, cross-linking a corpus too large for one person to hold. A proof assistant signs the certificate, and its 60 percent pass rate is what turns model output into usable fact. Contracts, lab notebooks, case law or code: wherever the source is already transcribed and the output is mechanically checkable, the same three layers apply.
The nine years of deciphering do not compress. Claude's two-day digest exists because that text layer existed first, and the scarce input was expert labor, with the model and the checker cast in supporting roles.
Key Takeaways
- University of Helsinki logician Jan von Plato's team has worked since 2017 on Gödel's 16 workbooks: 1,009 pages from the early 1940s, much of it in obsolete Gabelsberger shorthand. Human pace: about a page a week, roughly 50 pages a year.
- Given von Plato's transcriptions, his six earlier books on Gödel and the secondary literature, Claude produced a 650-page digest of the entire corpus in a couple of days, controlled page for page by the team.
- Claude extracted 663 theorem candidates. Coq verified about 400 as stated, repaired about 200, and found about 50 false. Gödel's own margins carry "falsch!" and "schlecht!" on his earlier self-corrections.
- Claude's reconstruction of the independence proof for the axiom of choice that Gödel claimed in 1966 passed Coq, with one wrong definition and the correct one two years earlier in the same notebooks. Paul Cohen won the Fields Medal for that result in 1966.
- On Claude's reading, the workbooks hold dozens of anticipations of results unknown until the 1970s and 80s, and 14 unpursued themes in logic. Von Plato plans to move on to Gödel's physics and cosmology notebooks next.
- Notre Dame's Joel David Hamkins, who has not seen the reconstruction: remarkable if it stands, and "how much is Claude and how much is Gödel is a job for the historians."
Sources: The Guardian, Nov 13, 2026, EconoTimes, Nov 14, 2026, Coq, Jan von Plato, Can Mathematics Be Proved Consistent? (Springer, 2020).